You have two 'clipboards' in Linux.
The first is the one of which you speak, where you select text and it is pasted via `SHIFT``INSERT` or `Middle-Mouse`. This clipboard/buffer is very fickle and changes constantly. Be careful using this, especially with chat clients, because one day you'll paste your password into IRC.
The second is the standard `CTRL``C` and `CTRL``V`, or selecting **Copy** or **Paste** from a menu. This clipboard/buffer is not overwritten by the previous and should be used as a more trusted clipboard.
My recommendation is to utilize the second version of the clipboard more often.